Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
268 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C8×D7 | C2 | semidirect |
| 3. C3×C4×C7×C8 | C2 | semidirect |
| 4. C3×(C2×D7)⋊C8 | C2 | semidirect |
| 5. C3×C4⋊(C7⋊C8) | C2 | semidirect |
| 6. C8×D28 | C3 | direct (N × H) |
| 16. C2×C8×D7 | C2×C3 | semidirect |
| 18. C4×C7×C8 | C2×C3 | semidirect |
| 19. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 20. C4⋊(C7⋊C8) | C2×C3 | semidirect |
| 27. C3×D28 | C8 | direct (N × H) |
| 31. C3×C7×C8 | D4 | semidirect |
| 46. C3×C4×C8 | D7 | semidirect |
| 50. C2×C3×D7 | C2×C8 | semidirect |
| 52. C3×C4×C7 | C2×C8 | semidirect |
| 62. D28 | C3×C8 | direct (N × H) |
| 66. C7×C8 | C3×D4 | semidirect |
| 85. C4×C8 | C3×D7 | semidirect |
| 89. C2×D7 | C2×C3×C8 | semidirect |
| 91. C4×C7 | C2×C3×C8 | semidirect |
| 105. C3×C8 | D28 | direct (N × H) |
| 106. C3×C7 | C8×D4 | semidirect |
| 126. C3×C4 | C8×D7 | semidirect |
| 139. C8 | C3×D28 | direct (N × H) |
| 140. C7 | C3×C8×D4 | semidirect |
| 151. C4 | C3×C8×D7 | semidirect |
| 154. C3 | C8×D28 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D7 | 2 |
| C3×C4×D28 | 2 |
| C3×C4×C7×C8 | 2 |
| C3×(C2×D7)⋊C8 | 2 |
| C3×C4⋊(C7⋊C8) | 2 |
| C8×D28 | 3 |
| C3×C8×D4 | 7 |